Monday, June 16, 2014

When the good drives out the bad

There's a fairly regular monetary phenomenon that needs a name. It's similar in nature to Gresham's law, yet the inverse version.

Gresham's law is commonly stated as the phenomena by which "bad money drives out the good". But as any economist will tell you, that's not quite it. Bad money chases out the good, but only if authorities have chosen to enforce a fixed exchange rate between the two moneys. When the market ratio diverges from the fixed ratio, the undervalued money—the "good" one—will disappear from circulation while the overvalued money —the bad one—will become the exchange medium of choice. Bad money drives out good money because they pass by law at the same fixed price.

That's the classic Gresham's law. However, it's possible to show how an authority can set a fixed price between two moneys yet rather than the bad coin chasing out the good, the opposite happens: the good coin chases out the bad.

Before I show how, let's first give an example of Gresham's law. Say that new full-bodied silver coins and debased silver coins with the same face value circulate concurrently. If authorities set a law requiring that all coins must be accepted by the populace at face value, buyers and debtors will only settle their bills in debased silver coin (the "bad" money). Full-bodied coins (the "good" money) will be held back as hoarders clip off a bit of each coin's silver content, converting the entire full-bodied coinage into debased coinage. After all, why spend x ounces of silver on goods when a smaller amount will suffice? Thus the bad chases out the good.

Now let's vary our example to have good money chase out the bad. Say authorities promise two-way conversion between all silver coins at face value. Everyone will bring debased silver coins, the "bad" money, to the authorities for conversion into full bodied coins, the "good" money. In essence, they are bringing in x ounces of silver and leaving with x + y silver. This will continue until every bad coin has been deposited into the authority's vaults so that only the good money circulates.

So why in the first case does bad silver coin chase out good yet in the second good chases out bad?

When coins circulate at face value while their true market price differs, a mispricing is created. Any mispricing provides an arbitrage opportunity. In our first example, the arbitrage is such that all those holding full-bodied coin can take a full-bodied coin, file off some silver, and purchase the same amount of goods as before with the now debased coin, all the while keeping the silver clippings to themselves. A different sort of arbitrage opportunity arises in our second example. Because the authorities offer a two-way conversion feature, everyone holding debased coins gets to enjoy a risk-free return by bringing those coins in for conversion into full-bodied coins. They get more silver with less.

So the way that the arbitrage opportunity is structured will either incentivize the population to switch to bad money or to good. We get Gresham's law if people switch en masse to bad coins, and we get an inverse-Gresham effect if they take advantage of conversion and switch en masse to good coins. Since I'm not feeling especially creative, I'll call this effect Mahserg's law (Gresham spelt backwards).

My favorite modern example of Gresham's law is the proliferation of credit cards. In the same way that an owner of a full bodied coin could clip a bit of "bonus" silver off the coin while still being guaranteed the same purchasing power, payment with a credit card allows its owner to maintain their purchasing power while getting rewards to boot.

There are a few modern examples of Masherg's law. In 1978 U.S. authorities created a situation in which two different exchange media with the same denomination circulated concurrently, the Susan B. Anthony dollar and the good old $1 US bill. Because it was novel and untrusted, the Susan B. Anthony was considered to be "bad" money. The dollar bill, which enjoyed network externalities that had been established over a century of use, was the "good" money. The Federal Reserve offered two-way conversion between coin and paper. The inevitable result was that whatever Susan B. Anthony dollars were emitted into the economy were quickly brought back to the Fed to be converted into paper dollars. The good money drove out the bad. To this day Susan B. Anthony dollars are nowhere to be seen.

Another example of Masherg's law is a good old bank run. Take the intra-Eurosystem bank run that began after the credit crisis. There exist many different brands of euros, some issued by Germany, some by Greece. As a condition of membership in the Eurosystem, all nations are required to accept each other's euros at par. With the spectre of euro breakup growing in 2010 and 2011, Greek euros came to be viewed as inferior to German euros. Since it was possible to convert the bad into the good at par, everyone leaped at the opportunity. The quantity of bad Greek euros rapidly contracted while the quantity of good German euros grew, a process that would have eventually resulted in the complete extinction of Greek euros if Mario Draghi hadn't stepped in to short-circuit the run.

My favorite modern example of Masherg's law is the zero-lower bound. A central bank issues two media, dollar bills and dollar deposits. It allows free conversion between the two at par. Say that the central bank reduces the interest rate it pays on reserves to a negative rate so that reserves are inferior, or "bad", relative to 0%-yielding bills, which are now good. Anxious to avoid the negative rate penalty, everyone will race to convert their reserves into cash at the central bank until reserves no longer exist. The good has chased out the bad.

The zero-lower bound can be thought of as the lowest rate that a central bank can institute before setting off Masherg's law. Modern central banks are petrified of encountering this particular law—that's one reason that they aim for a positive inflation target

And what about Gresham? Say our central bank reduces rates below zero. If the central bank ceases allowing convertibility between dollar notes and deposits but continues to require merchants to accept the two media at par, then the incentives change such that the good no longer chases out the bad. With no conversion outlet for bad currency, people will hoard notes while only deposits will circulate. After all, why use good cash to pay for groceries when a negative yielding deposit will suffice? We're back at Gresham's law, or the chasing out of the good by the bad.

10 comments:

This seems like a tortured way around explicitly arguing the inverse, that negative interest rates will not chase out good money, b/c notes and deposits are fully convertible. If that is your real agenda, why not just say so. Or maybe I'm reading too much into it. Logically what you've said is not equivalent to its inverse, and I could be trying to hard to make it into something more interesting.

Real agenda, as in my hidden agenda? I don't think I've got one in this post (although I do think it would be wise to allow central banks to set negative rates and thereby by avoid hitting Mahserg's law). The inverse of the bad chasing out the good is the good chasing out the bad -- I'm just exploring what sort of rule drives the one rather than the other.

After puzzling over wikipedia on logical propositions, I think you are describing the converse not the inverse. But one implies the other. Anyway, the reason Gresham's law works is b/c there is some real barrier for the accepting party to differentiate between good and bad money. There's no law that one must accept counterfeit coinage, but it passes alongside legit money b/c of the physical similarity and the relatively high cost of detecting counterfeits (relative to routine transactions). In the context of deposits, the analogy to Gresham is for deposits at competing institutions where there is fundamentally different underlying quality in the asset, but not in a way that is visible to the depositor. I don't think that you can draw any new conclusion from consumer preference for deposits vs. notes based on interest rates, even with the assumption that deposits are frozen. A law requiring merchants to accept crappy deposit certificates at par to notes would fail. People would circumvent it.

Gresham's law applies equally well to a bimetallic system in which it is easy to quickly spot the difference between good and bad money (either the gold coinage or silver coinage will be undervalued). Legal tender laws required that debts be paid in either of the two at a fixed ratio.

We know from historical examples that in bimetallic systems, undervalued coins were typically hoarded and sent overseas, the overvalued coins circulating. That's why medieval economies would often whipsaw back and forth between gold or silver metallic systems. If the populace had chosen to ignore legal tender laws and only accepted coin at their true market value, then these whipsaws would not have occurred.

In the modern case of negative yielding deposits, we could of course argue that merchants and debtors might ignore legal tender laws and only accept bad deposits at a discount relative to cash. But the bimetallic example shows that the converse (inverse?) also applies; people may choose to obey the laws. If so, we would see a Gresham effect where only bad deposits circulate, just as we saw overvalued gold coin replacing silver in circulation.

There must be some equilibrium between assets. If a bank can charge interest to hold your deposits without triggering a run, that is b/c there is some comparative advantage (even an artificial one like maintaining regulatory capital) to holding some wealth in deposits.

Is see, in this Thier's law the wiki authors only seem to be talking about long run values and hence the relevance of the law in inflationary episodes. Though I'm not so sure that part of the analysis is that removed from yours.

1. Given the extreme slowness of the withdrawal of euros from Greece, can we really call it a run? Are there any other examples of runs that take years to play out?

2. In Spain and Italy, the largest monthly 'runs' occurred in March, 2012. That was the lowest stress month, as evinced by sovereign yields, for nearly a year. In Spain, the reserve movement was four times as large in March as it was in November, an indisputably stressed month. Do you have a thought as to why the 'run' of euros from the periphery does not occur when stress is high? This question has been posed elsewhere as a riddle: http://www.antehoc.com/2013/10/euro-zone-capital-flight-ny-fed-blog.html